The Linksys wireless router in the middle of it all is the thing you need to worry about, but it should be able to handle at least 16 unique devices without a problem. I've not heard of a consumer device with such a low limit in *ages*.
It's good that you have a switch dedicated to your office computers. When they're talking to each other and not to the internet they won't even need to send traffic to the upstream wireless router. If it's not a gigabit router you may want to look into it if you often send files between computers. (The computers will also need gigabit ethernet adapters to take advantage, though.)
Everything looks good. Do your devices currently use dhcp to get the ip addresses? If so, everything might "just work" with the new setup.
